/sci/ - Science & Math

>>9175745
So far AG is 0/1 on solving millennium prize problems.

>>9175745
if you solve P=NP with alg geo i might actually suck your dick in real life and i know at least three other tenured faculty who would do the same

No

>>9175745

no current math can solve them. You'd have to invent a whole new branch of mathematics to solve any of these problems, that's the whole point...

I don't think so

>>9175808
Perelman solved with PDEs and I used hyperreal numbers [math]^\star\mathbb{R}[/math]to (hopefully) disprove the Riemann hypothesis. PDEs and hyperreals have been around for a long time.

>On The Riemann Zeta Function
>http://vixra.org/abs/1703.0073

>muh schemes
>muh sheaves
>muh varieties
>solving anything
Remember when geometry was about homologies/homotopies and metrics? Fucking millennials ruining math.

>>9175839
> Muh motive

>>9175839
>muh metric theory
kys :^)

Infact, I think the solution to P?=NP will be a geometric one. We will be able to find some fundamental parameters of problems by some topology magic can show that there are problems that are in NP but not in P.

>>9175745
All of these problems are trivial assuming 57 is prime

>>9175771
The only reason P=NP hasn't been solved yet is because computer scientists are fucking brainlets. We just need ONE bright mathematician to tackle it and it'll be done.

>>9175839
Remember when geometry was about circles and triangles and angles? Fucking modernists ruining math.

>>9176442
P=NP people tried use set theory with complexity class and found some weird trick, but maybe begin need rebuild idea algorithm to solved P=NP.

What is the positive outcome or usefulness of having the solution to these problems?

>>9176442
I dont care who solves, might even be a sociologist... Just solve it already! This is considered by many to be the most important millenium problem, just get off of your arses pls ty

>>9176467
A million dollars.

>>9176475
The result is not that important, we already now that P!=NP. Even if somebody would formally prove it it wouldnt mean anything for computer science

you should be able to solve them all with ruler and compass

>>9175825
>Perelman solved with PDEs
Undergrad here. I know what PDEs are and know how to solve (some of) them but I lack the more advanced techniques to understand the proof. I didn't know he used DE's in his proof. I thought it was all topological sorcery. Is there any article that explains the concept of his proof with some technical details that aren't so technical an undergrad wouldn't understand it?

>>9177052
PDEs are used in topological sorcery, so you are not wrong.

>>9175825
Hello Jonathan

>>9177062
Sometimes I wish I could just disconnect from my brain, let my body go on autopilot for a couple of years, go on a deep sleep as it finishes my education, and then reconnect to my body after I already have a PhD.

It feels bad to know there is so much that other people know but you don't know :(

>>9177052
https://en.wikipedia.org/wiki/Ricci_flow

https://mathoverflow.net/questions/89748/what-prerequisites-do-i-need-to-read-the-book-ricci-flow-and-the-poincare-conjec

Book geometric topology
http://people.dm.unipi.it/martelli/Geometric_topology.pdf

>>9175825
>vixra

>>9177052
Here is some lectures:
>https://terrytao.wordpress.com/category/teaching/285g-poincare-conjecture/

>>9177052
This ...
http://www.claymath.org/library/monographs/cmim03.pdf

>>9177147
>>9177088
I'm too dumb for any of these but thank you.

>>9177187
>500 pages
"Overview of Perelman's argument" sounds good. Thank you.

>>9177052
The very rough overview of what perelman did was to change the manifold using a sort of generalized diffusion equation, this process being referred to as ricci flow. As you deform the manifold it ends up becoming the sphere, in fact you only need a finite amount of time to do it (the amount of time the evolution equation needs). There are some complications though, one being the fact that some of the manifolds end up deforming in such a way that they create singularities, you need to do something called surgery to get rid of them, then use the connected sum of the two components to add them back up. Another complication is that of solitons, basically these objects wouldn't disappear and thus impeded the flow, but perelman was able to get around that and show that the ricci flow process worked and thus these manifolds could be smoothly deformed into spheres.

>>9176442
I'm sorry to break it to you but bright mathematicans have tried and bright mathematicans have failed

my dept head is an alg geometer but I'm too much a brainlet to study with him. I think he's looking for a grad student but damn...I can barely remember the strong nulstellensatz

No.

>>9175808
That's not true

>>9177220
>deforming in such a way that they create singularities, you need to do something called surgery to get rid of them, then use the connected sum of the two components to add them back up.
Is this similar to the way that the proof of the quarter-pinched sphere theorem works? How you cut a simply connected manifold in half, prove that they're both homeomorphic to a disk, then glue them back together at the boundary to show that it was a sphere all along?

>>9177590
Kind of, you do surgery and cut out the singularity which then results in two separate components, but those will then collapse into spheres at which point you can take what is called the connected sum (the connected sum of two spheres is a sphere) and that gives you the desired result. Mind you that this is only when singularities form (they don't always). It's actually funny you mention the quarter-pinched sphere theorem, a stronger result called the differentiable sphere theorem was proven using ricci flow.

>>9177610
I guess I'll check out some types of (mathy) surgery. I've temporarily dropped out of school so I have nothing better to do.

>>9175745
No.

>>9177633
>I guess I'll check out some types of (mathy) surgery
Besides the other suggested texts one that I like that covers surgery is this one
http://www.maths.ed.ac.uk/~aar/papers/kosinski.pdf

>>9177646
Damn this is pretty cool. It's like a book of things that your smooth manifolds class tried to get you not to think about.

>>9177662
The book does have it's short comings though, for instance, no one really studies foliations anymore, not saying it's a dead subject, more just out of fashion, so it's not something you'd see in a more modern text. It also doesn't cover some exciting recent developments for obvious reasons.